856 citations · 1.9k across the 8 of their papers we have counts for
8 papers
Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture
Abhay Ashtekar, Adam Henderson, David Sloan
The Belinkskii, Khalatnikov and Lifshitz conjecture says that as one approaches space-like singularities in general relativity, 'time derivatives dominate over spatial derivatives'…
Geometrical Formulation of Quantum Mechanics
Abhay Ashtekar, Troy A. Schilling
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a Kähler manifold. This leads to a geom…
Asymptotic Structure of Symmetry Reduced General Relativity
Abhay Ashtekar, Jiri Bicak, Bernd G. Schmidt
Gravitational waves with a space-translation Killing field are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein eq…
Quantum Theory of Gravity I: Area Operators
Abhay Ashtekar, Jerzy Lewandowski
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry.…
Coherent State Transforms for Spaces of Connections
Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf +2
The Segal-Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Li…
Differential Geometry on the Space of Connections via Graphs and Projective Limits
Abhay Ashtekar, Jerzy Lewandowski
In a quantum mechanical treatment of gauge theories (including general relativity), one is led to consider a certain completion, $\agb$, of the space $\ag$ of gauge equivalent conn…